Ex - Max Limited Sequence

AtCoder

IDabc262_h

Time2000ms

Memory256MB

Difficulty—

Find the number, modulo $998244353$, of integer sequences $A = (A_1, \dots, A_N)$ of length $N$ that satisfy all of the following conditions: * $0 \leq A_i \leq M$ for all $i$ such that $1 \leq i \leq N$. * The maximum value of $A_{L_j}, \dots, A_{R_j}$ is $X_j$ for all $j$ such that $1 \leq j \leq Q$. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $1 \leq M \lt 998244353$ * $1 \leq Q \leq 2 \times 10^5$ * $1 \leq L_i \leq R_i \leq N \, (1 \leq i \leq Q)$ * $1 \leq X_i \leq M \, (1 \leq i \leq Q)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $Q$ $L_1$ $R_1$ $X_1$ $\vdots$ $L_Q$ $R_Q$ $X_Q$ [samples]

Samples

Input #1

3 3 2
1 2 2
2 3 3

Output #1

5

$A = (0, 2, 3), (1, 2, 3), (2, 0, 3), (2, 1, 3), (2, 2, 3)$ satisfy the conditions.

Input #2

1 1 1
1 1 1

Output #2

Input #3

6 40000000 3
1 4 30000000
2 6 20000000
3 5 10000000

Output #3

135282163

API Response (JSON)

{
  "problem": {
    "name": "Ex - Max Limited Sequence",
    "description": {
      "content": "Find the number, modulo $998244353$, of integer sequences $A = (A_1, \\dots, A_N)$ of length $N$ that satisfy all of the following conditions: *   $0 \\leq A_i \\leq M$ for all $i$ such that $1 \\leq i \\",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc262_h"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Find the number, modulo $998244353$, of integer sequences $A = (A_1, \\dots, A_N)$ of length $N$ that satisfy all of the following conditions:\n\n*   $0 \\leq A_i \\leq M$ for all $i$ such that $1 \\leq i \\...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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